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All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

STRATEGIES IN SEISMIC INFERENCE OF SUPERGRANULAR FLOWS ON THE SUN

Observations of the solar surface reveal the presence of flows with length scales of around 35 Mm, commonly referred to as supergranules. Inferring the subsurface flow profile of supergranules from measurements of the surface and photospheric wavefield is an important challenge faced by helioseismology. Traditionally, the inverse problem has been approached by studying the linear response of seismic waves in a horizontally translationally invariant background to the presence of the supergranule; following an iterative approach that does not depend on horizontal translational invariance might perform better, since the misfit can be analyzed post iterations. In this work, we construct synthetic observations using a reference supergranule and invert for the flow profile using surface measurements of travel times of waves belonging to modal ridges f (surface gravity) and p {sub 1} through p {sub 7} (acoustic). We study the extent to which individual modes and their combinations contribute to infer the flow. We show that this method of nonlinear iterative inversion tends to underestimate the flow velocities, as well as inferring a shallower flow profile, with significant deviations from the reference supergranule near the surface. We carry out a similar analysis for a sound-speed perturbation and find that analogous near-surface deviations persist, although the iterations converge faster and more accurately. We conclude that a better approach to inversion would be to expand the supergranule profile in an appropriate basis, thereby reducing the number of parameters being inverted for and appropriately regularizing them.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1975

Spinning mode sound propagation in ducts with acoustic treatment

Recent acoustic data show larger noise attenuations than predicted for acoustically treated aircraft engine inlets without splitter rings. A theoretical study of the acoustic propagation of spinning modes in acoustically treated open circular ducts is presented, and a suppressor with splitter rings was modeled by using the rectangular approximation to the annular duct. Theoretical models were used to determine optimum impedance and maximum attenuation for several spinning lobe numbers from 0 to 50. Results of the analysis indicate that for circular ducts the maximum possible attenuation and the optimum wall impedance are strong functions of the lobe number, and for annular ducts the attenuation and optimum wall impedance are insensitive to the spinning lobe number for well cut-on modes. These results explain why suppressors with splitter rings were quite effective in spite of the lack of detailed information on the noise source modal structure. Conversely, effective use of outer wall treatment alone will require expanded knowledge of the noise source structure. Approximate solutions are presented to help interpret the more exact theoretical results.

Rice, E. J.↗
NASA NTRS1990

Approach to large space structure control system design using traditional tools

This paper illustrates how traditional analysis and design tools can be successfully applied, with insights derived from recent research on control-structure interaction, to preliminary control system design for a large space structure such as the Space Station Freedom. The control system regulates attitude during construction, normal on-orbit operation, reboost, and docking using control-moment gyros and thrusters. The tools include finite-element modeling, model reduction based on modal truncation, single-input/single-output Bode plot design, position and rate feedback, roll-off and phase filter, and simulation. The resulting system is characterized by simple architecture and moderate bandwidth. The large configuration changes during the construction period are handled by gain scheduling.

Chu, P. Y.↗
DOE OSTI2014

Video-rate optical dosimetry and dynamic visualization of IMRT and VMAT treatment plans in water using Cherenkov radiation

Purpose: A novel technique for optical dosimetry of dynamic intensity-modulated radiation therapy (IMRT) and volumetric-modulated arc therapy (VMAT) plans was investigated for the first time by capturing images of the induced Cherenkov radiation in water. Methods: A high-sensitivity, intensified CCD camera (ICCD) was configured to acquire a two-dimensional (2D) projection image of the Cherenkov radiation induced by IMRT and VMAT plans, based on the Task Group 119 (TG-119) C-Shape geometry. Plans were generated using the Varian Eclipse treatment planning system (TPS) and delivered using 6 MV x-rays from a Varian TrueBeam Linear Accelerator (Linac) incident on a water tank doped with the fluorophore quinine sulfate. The ICCD acquisition was gated to the Linac target trigger pulse to reduce background light artifacts, read out for a single radiation pulse, and binned to a resolution of 512 × 512 pixels. The resulting videos were analyzed temporally for various regions of interest (ROI) covering the planning target volume (PTV) and organ at risk (OAR), and summed to obtain an overall light intensity distribution, which was compared to the expected dose distribution from the TPS using a gamma-index analysis. Results: The chosen camera settings resulted in 23.5 frames per second dosimetry videos. Temporal intensity plots of the PTV and OAR ROIs confirmed the preferential delivery of dose to the PTV versus the OAR, and the gamma analysis yielded 95.9% and 96.2% agreement between the experimentally captured Cherenkov light distribution and expected TPS dose distribution based upon a 3%/3 mm dose difference and distance-to-agreement criterion for the IMRT and VMAT plans, respectively. Conclusions: The results from this initial study demonstrate the first documented use of Cherenkov radiation for video-rate optical dosimetry of dynamic IMRT and VMAT treatment plans. The proposed modality has several potential advantages over alternative methods including the real-time nature of the acquisition, and upon future refinement may prove to be a robust and novel dosimetry method with both research and clinical applications.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2015

SU-E-J-42: Evaluation of Fiducial Markers for Ultrasound and X-Ray Images Used for Motion Tracking in Pancreas SBRT

Purpose Ultrasound tracking of target motion relies on visibility of vascular and/or anatomical landmark. However this is challenging when the target is located far from vascular structures or in organs that lack ultrasound landmark structure, such as in the case of pancreas cancer. The purpose of this study is to evaluate visibility, artifacts and distortions of fusion coils and solid gold markers in ultrasound, CT, CBCT and kV images to identify markers suitable for real-time ultrasound tracking of tumor motion in SBRT pancreas treatment. Methods Two fusion coils (1mm × 5mm and 1mm × 10 mm) and a solid gold marker (0.8mm × 10mm) were embedded in a tissue–like ultrasound phantom. The phantom (5cm × 12cm × 20cm) was prepared using water, gelatin and psyllium-hydrophilic-mucilloid fiber. Psylliumhydrophilic mucilloid acts as scattering medium to produce echo texture that simulates sonographic appearance of human tissue in ultrasound images while maintaining electron density close to that of water in CT images. Ultrasound images were acquired using 3D-ultrasound system with markers embedded at 5, 10 and 15mm depth from phantom surface. CT images were acquired using Philips Big Bore CT while CBCT and kV images were acquired with XVI-system (Elexta). Visual analysis was performed to compare visibility of the markers and visibility score (1 to 3) were assigned. Results All markers embedded at various depths are clearly visible (score of 3) in ultrasound images. Good visibility of all markers is observed in CT, CBCT and kV images. The degree of artifact produced by the markers in CT and CBCT images are indistinguishable. No distortion is observed in images from any modalities. Conclusion All markers are visible in images across all modalities in this homogenous tissue-like phantom. Human subject data is necessary to confirm the marker type suitable for real-time ultrasound tracking of tumor motion in SBRT pancreas treatment.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Machine Learning Enabled Sensor Fusion for In-Situ Defect Detection in Laser Powder Bed Fusion

Laser Powder Bed Fusion (L-PBF) Additive Manufacturing (AM) is among the metal 3D printing technologies most broadly adopted by the manufacturing industry. The current industry qualification paradigm for critical-application L-PBF parts relies heavily on expensive non-destructive inspection techniques such as X-Ray Computed Tomography (XCT), which significantly limits the use-cases of L-PBF. In situ monitoring of the process promises a less expensive alternative to ex situ testing, but existing sensor technologies and data analysis techniques struggle to detect sub-surface flaws (e.g., porosity and cracking) on production-scale L-PBF printers. RTX Technologies Research Center (RTRC) has licensed ORNL’s Peregrine software package – a printer- and camera-agnostic data analytics tool designed specifically for detecting process anomalies using in situ data collected during powder bed printing. The goal of this project was to feed temporally rich, multi-modal sensor data, including visible light, integrated near infrared (NIR), and spatially mapped co-axial melt pool thermal emission data into Peregrine to enable detection of subsurface flaws. XCT data was used as ground truth training data to allow Peregrine’s deep learning algorithms to recognize anomalies in these complex data streams in both test artifacts and industrially relevant geometries. Completion of this program has seen the successful implementation of multi-modal, multi-layer sensor data footprints for training of machine learning models in Peregrine. Flaws detected in XCT data have been successfully detected directly from this in situ data footprint, and initial analyses of the in situ probability-of-detection has been conducted, showing performance levels commensurate with traditional non-destructive evaluation (NDE) methods. The in situ monitoring methodology was then applied to an industrially relevant component that was using post-build NDE, highlighting the utility of the proposed method for hard-to-inspect AM components. As a direct result of this program, two journal manuscripts [1], [2] have been published in Additive Manufacturing, with additional manuscripts planned following program completion.

36 MATERIALS SCIENCE↗
NASA NTRS1974

Spinning mode sound propagation in ducts with acoustic treatment

A detailed theoretical study of the acoustic propagation of spinning modes in acoustically treated open circular ducts is described. The suppressor with splitter rings was modeled by using the rectangular approximation to the annular duct. The theoretical models were used to determine optimum impedance and maximum attenuation for several spinning lobe numbers from 0 to 50. Some interesting results of the analysis are that for circular ducts the maximum possible attenuation and the optimum wall impedance are strong functions of the lobe number. For annular ducts the attenuation and optimum wall impedance are insensitive to the spinning lobe number for well cut-on modes. The above results help explain why suppressors with splitter rings were quite effective in spite of the lack of detailed information on the noise source modal structure.

Rice, E. J.↗
NASA NTRS1999

Acoustic Reflection and Transmission of 2-Dimensional Rotors and Stators, Including Mode and Frequency Scattering Effects

A reduced order modeling scheme has been developed for the unsteady acoustic and vortical coupling between blade rows of a turbomachine. The essential behavior of the system is governed by modal scattering coefficients (i.e., reflection and transmission coefficients) of the rotor, stator, inlet and nozzle, which are calculated as if they were connected to non-reflecting ducts. The objective of this report is to identify fundamental behavior of these scattering coefficients for a better understanding of the role of blade row reflection and transmission in noise generation. A 2D flat plate unsteady cascade model is used for the analysis with the expectation that the general behavior presented herein will carry over to models that include more realistic flow and geometry. It is shown that stators scatter input waves into many modes at the same frequency whereas rotors scatter on frequency, or harmonic order. Important cases are shown here the rotor reflection coefficient is greater than unity; a mode at blade passing frequency (BPF) traveling from the stator with unit sound power is reflected by the rotor with more than unit power at 2xBPF and 3xBPE Analysis is presented to explain this unexpected phenomenon. Scattering curves are presented in a format chosen for design use and for physical interpretation. To aid in interpretation of the curves, formulas are derived for special condition where waveforms are parallel to perpendicular to the rotor.

Hanson, Donald B.↗
NASA NTRS2008

New Insights into the Composition and Texture of Lunar Regolith Using Ultrafast Automated Electron-Beam Analysis

Sieved grain mounts of Apollo 16 drive tube samples have been examined using QEMSCAN - an innovative electron beam technology. By combining multiple energy-dispersive X-ray detectors, fully automated control, and off-line image processing, to produce digital mineral maps of particles exposed on polished surfaces, the result is an unprecedented quantity of mineralogical and petrographic data, on a particle-by-particle basis. Experimental analysis of four size fractions (500-250 microns, 150-90 microns, 75-45 microns and < 20 microns), prepared from two samples (64002,374 and 64002,262), has produced a robust and uniform dataset which allows for the quantification of mineralogy; texture; particle shape, size and density; and the digital classification of distinct particle types in each measured sample. These preliminary data show that there is a decrease in plagioclase modal content and an opposing increase in glass modal content, with decreasing particle size. These findings, together with data on trace phases (metals, sulphides, phosphates, and oxides), provide not only new insights into the make-up of lunar regolith at the Apollo 16 landing site, but also key physical parameters which can be used to design lunar simulants, and compute Figures of Merit for each material produced.

Rickman, Doug↗
NASA NTRS2008

Lunar Dust Effects on Spacesuit Systems: Insights from the Apollo Spacesuits

Systems and components of selected Apollo A7L/A7LB flight-article spacesuits that were worn on the lunar surface have been studied to determine the degree to which they suffered contamination, abrasion and wear or loss of function due to effects from lunar soil particles. Filter materials from the lithium hydroxide (LiOH) canisters from the Apollo Command Module were also studied to determine the amount and type of any lunar dust particles they may have captured from the spacecraft atmosphere. The specific spacesuit study materials include the outermost soft fabric layers on Apollo 12 and 17 integrated thermal micrometeorite garment assemblies and outermost fabrics on Apollo 17 extravehicular pressure gloves. In addition, the degree of surface wear in the sealed wrist rotation bearing from Apollo 16 extravehicular and intravehicular pressure gloves was evaluated and compared. Scanning electron microscope examination of the Apollo 12 T-164 woven TeflonO fabric confirms the presence of lunar soil particles and the ability of these particles to cause separation and fraying of the Teflon fibers. Optical imaging, chemical analysis and particle sampling applied to the outer fabric of the Apollo 17 spacesuit has identified Ti as a potentially useful chemical marker for comparing the amount of lunar soil retained on different areas of the spacesuit outer fabric. High-yield particle sampling from the Apollo 17 fabric surfaces using adhesive tape found 80% of particles on the fabric are lunar soil particles averaging 10.5 m in diameter, with the rest being intrinsic fabric materials or environmental contaminants. Analysis of the mineralogical composition of the lunar particles found that on a grain-count basis the particle population is dominated by plagioclase feldspar and various types of glassy particles derived mostly from soil agglutinates, with a subordinate amount of pyroxene. On a grain size basis, however, the pyroxene grains are generally a factor of 2 larger than glass and plagioclase, so conversion of the data to a modal (volume %) basis results in pyroxene becoming the modally dominant particle type with glass and plagioclase significantly less abundant. When comparisons are made to the modal composition of lunar soil at the Apollo 17 landing site, the results suggest that pyroxene particles have overall better retention on the spacesuit outer fabric compared to plagioclase and especially glass. Scanning electron microscopy revealed no measureable difference in the amount of wear and abrasion in the wrist rotation bearing of an Apollo 16 pressure glove worn only in the spacecraft and one worn only for extravehicular activity on the lunar surface. The results suggest either that the bearing prevented entry of lunar dust, or that dust was not sufficiently abrasive to damage the bearing, or both.

Christoffersen, Roy↗
NASA NTRS1992

First results from analysis of coordinated AVIRIS, TIMS, and ISM (French) data for the Ronda (Spain) and Beni Bousera (Morocco) peridotites

Ultramafic rocks are relatively rare at the Earth's surface but constitute the vast majority of the Earth by volume. Exposures of ultramafic bodies are therefore crucial for deducing many important processes that occur in the Earth's mantle. An important science question regarding the spatial distribution, abundance, and composition of mafic minerals in ultramafic bodies that can be examined with advanced sensor data is the melting process. When a lherzolite melts, clinopyroxene (cpx) melts first and therefore variations in the modal amount of cpx remaining in the mantle are a reflection of the amount of fractional melting that has occurred. Fe goes preferentially into the melt during melting but a 20 percent batch melting (i.e. closed system) acquires less Fe relative to 20 percent fractional melting (i.e. open system). Since the strength and wavelength of diagnostic absorptions is a strong function of Fe content, it is possible to make maps of the variation in Fe:Mg ratios which can be related to the general melting process. Accurate ground-truth information about local mineralogy provides internal calibration and consistency checks. Investigations using imaging spectrometer are very complementary to field studies because advanced sensor data can provide a synoptic view of modal mineralogy and chemical composition whereas field studies focus on detailed characterization of local areas. Two excellent exposures of ultramafic lithologies are being investigated with visible to mid-infrared imaging spectrometer data: the Ronda peridotite near Ronda, Spain and the Beni Bousera ophiolitic fragment in northern Morocco. Although separated by the Alboran Sea, these bodies are thought to be related and represent fertile sub-continental mantle. The Ronda peridotite is predominantly spinel lherzolite but grades into harzburgite and shows considerable variation in major and trace element compositions. Mafic layering and dykes (i.e. olivine gabbro) are also observed. This indicates some sections of the peridotite have experienced greater degrees of partial melting. The Beni Bousera peridotite also contains mafic layers and dykes and grades into harzburgite representing similar fundamental shifts in the bulk chemistry of this ultramafic body probably related to an episode of partial melting. The specific mode of emplacement of these bodies is controversial and important for understanding the tectonic evolution of this region. Our investigations are not necessarily designed to help resolve this controversy. Rather, these exposures provide excellent and unusual examples of fertile mantle which have undergone variable degrees of partial melting.

Mustard, J. F.↗
DOE OSTI2020

SMART Mobility. Modeling Workflow Development, Implementation, and Results Capstone Report

The U.S. Department of Energy’s Systems and Modeling for Accelerated Research in Transportation (SMART) Mobility Consortium is a multiyear, multi-laboratory collaborative, managed by the Energy Efficient Mobility Systems Program of the Office of Energy Efficiency and Renewable Energy, Vehicle Technologies Office, dedicated to further understanding the energy implications and opportunities of advanced mobility technologies and services. The first three-year research phase of SMART Mobility occurred from 2017 through 2019, and included five research pillars: Connected and Automated Vehicles, Mobility Decision Science, Multi-Modal Freight, Urban Science, and Advanced Fueling Infrastructure. A sixth research thrust integrated aspects of all five pillars to develop a SMART Mobility Modeling Workflow to evaluate new transportation technologies and services at scale. This report summarizes the work of the SMART Mobility Modeling Workflow effort. The SMART Mobility Modeling Workflow was developed to evaluate new transportation technologies such as connectivity, automation, sharing, and electrification through multi-level systems analysis that captures the dynamic interactions between technologies. By integrating multiple models across different levels of fidelity and scale, the Workflow yields insights about the influence of new mobility and vehicle technologies at the system level. For information about the other Pillars, please refer to the relevant pillar’s Capstone Report.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2015

A comparative numerical analysis of linear and nonlinear aerodynamic sound generation by vortex disturbances in homentropic constant shear flows

Aerodynamic sound generation in shear flows is investigated in the light of the breakthrough in hydrodynamics stability theory in the 1990s, where generic phenomena of non-normal shear flow systems were understood. By applying the thereby emerged short-time/non-modal approach, the sole linear mechanism of wave generation by vortices in shear flows was captured [G. D. Chagelishvili, A. Tevzadze, G. Bodo, and S. S. Moiseev, “Linear mechanism of wave emergence from vortices in smooth shear flows,” Phys. Rev. Lett. 79, 3178-3181 (1997); B. F. Farrell and P. J. Ioannou, “Transient and asymptotic growth of two-dimensional perturbations in viscous compressible shear flow,” Phys. Fluids 12, 3021-3028 (2000); N. A. Bakas, “Mechanism underlying transient growth of planar perturbations in unbounded compressible shear flow,” J. Fluid Mech. 639, 479-507 (2009); and G. Favraud and V. Pagneux, “Superadiabatic evolution of acoustic and vorticity perturbations in Couette flow,” Phys. Rev. E 89, 033012 (2014)]. Its source is the non-normality induced linear mode-coupling, which becomes efficient at moderate Mach numbers that is defined for each perturbation harmonic as the ratio of the shear rate to its characteristic frequency. Based on the results by the non-modal approach, we investigate a two-dimensional homentropic constant shear flow and focus on the dynamical characteristics in the wavenumber plane. This allows to separate from each other the participants of the dynamical processes — vortex and wave modes — and to estimate the efficacy of the process of linear wave-generation. This process is analyzed and visualized on the example of a packet of vortex modes, localized in both, spectral and physical, planes. Further, by employing direct numerical simulations, the wave generation by chaotically distributed vortex modes is analyzed and the involved linear and nonlinear processes are identified. The generated acoustic field is anisotropic in the wavenumber plane, which results in highly directional linear sound radiation, whereas the nonlinearly generated waves are almost omni-directional. As part of this analysis, we compare the effectiveness of the linear and nonlinear mechanisms of wave generation within the range of validity of the rapid distortion theory and show the dominance of the linear aerodynamic sound generation. Finally, topological differences between the linear source term of the acoustic analogy equation and of the anisotropic non-normality induced linear mechanism of wave generation are found.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Exploring urban typologies using comprehensive analysis of transportation dynamics

Abstract As urban areas continue to expand and develop, categorizing cities into typologies offers a valuable framework for understanding metropolitan dynamics and fostering inter-city collaboration. However, existing typologies related to urban mobility have limitations, failing to consider cities within a single large urban region and often overlooking crucial dimensions such as trip demand and traffic flow. In this paper, we introduce a transportation-focused characterization for cities within a large urban region, specifically the San Francisco Bay Area, California. We incorporate over 40 metrics across five transportation dimensions: trip demand, road network, multi-modal network, traffic flow, and land use. Specifically, for the trip demand dimension, we include metrics capturing residents’ trip characteristics, such as mode share, intra-city trips, and inter-city trips. Additionally, we analyze the purpose of trips entering the city to gain a deeper understanding of incoming trip patterns. In the traffic flow dimension, we examine metrics like vehicle miles traveled, delay, and congestion to assess the traffic conditions on the street network. These, combined with other dimensions, provide a comprehensive view of a city’s transportation dynamics. Using unsupervised machine learning clustering methods, we identified eight distinct typologies for the Bay Area: Live Work Cities; Job and Activity Magnet Cities; Anchor Cities; Multi-modal Cities; Hyper-connected Cities; Low-density Residential Cities; Medium-density Residential Cities; and Mixed-use Residential Cities. Our findings show that many clusters are strongly influenced by trip demand and traffic flow metrics. Finally, we examine the practicality of this typology and its potential to guide collaborative transportation management strategies. The typologies provide a foundation for dialogue among Bay Area cities, focusing on evaluating shared characteristics and leveraging successes or challenges to develop unified strategies for transportation management.

Kuncheria, Anu↗
DOE OSTI2016

Better Efficacy of Synchrotron Spatially Microfractionated Radiation Therapy Than Uniform Radiation Therapy on Glioma

Purpose: Synchrotron microbeam radiation therapy (MRT) is based on the spatial fractionation of the incident, highly focused synchrotron beam into arrays of parallel microbeams, typically a few tens of microns wide and depositing several hundred grays. This irradiation modality was shown to have a high therapeutic impact on tumors, especially in intracranial locations. However, mechanisms responsible for such a property are not fully understood. Methods and Materials: Thanks to recent progress in dosimetry, we compared the effect of MRT and synchrotron broad beam (BB) radiation therapy delivered at comparable doses (equivalent to MRT valley dose) on tumor growth control and on classical radiobiological functions by histologic evaluation and/or transcriptomic analysis. Results: MRT significantly improved survival of rats bearing 9L intracranial glioma compared with BB radiation therapy delivered at a comparable dose (P<.001); the efficacy of MRT and BB radiation therapy was similar when the MRT dose was half that of BB. The greater efficacy of MRT was not correlated with a difference in cell proliferation (Mki67 and proliferating cell nuclear antigen) or in transcriptomic stimulation of angiogenesis (vascular endothelial growth factor A or tyrosine kinase with immunoglobulin-like and epidermal growth factor-like domains 2) but was correlated with a higher cell death rate (factor for apoptosis signals) and higher recruitment of macrophages (tyrosine kinase with immunoglobulin-like and epidermal growth factor-like domains 1 and CD68 transcripts) a few days after MRT. Conclusions: These results show the superiority of MRT over BB radiation therapy when applied at comparable doses, suggesting that spatial fractionation is responsible for a specific and particularly efficient tissue response. The higher induction of cell death and immune cell activation in brain tumors treated by MRT may be involved in such responses.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
NASA NTRS1987

Centaur G Prime modal test

The Centaur G Prime modal test resulted in sets of modes (frequencies, mode shapes and damping) with an accuracy similiar to or better than that normally obtained from the modal testing of linear structures with no backlash and small damping. In other words, performing the test at high level greatly minimized the backlash effect and provided a valid, simple linearization of the trunnion friction problem for the Centaur in the Shuttle Cargo Bay. All the most important modes (target modes) were measured and provided the data base for updating the finite element model for the pre-flight verification loads analysis.

Trubert, Marc↗
NASA NTRS1988

Dynamic structural correlation via nonlinear programming techniques

A solution to the correlation between structural dynamic test results and finite element analyses of the same components is presented in this paper. Basically, the method can be categorized as a Levenberg-Marquardt type Gauss-Newton method which requires only the differences between FE modal analyses and test results and their first derivatives with respect to preassigned design variables. With proper variable normalization and equation scaling, the method has been made numerically better-conditioned and the inclusion of the Levenberg-Marquardt technique overcomes any remaining difficulty encountered in inverting singular or near-singular matrices. An important feature is that each iteration requires only one function evaluation along with the associated design sensitivity analysis and so the procedure is computationally efficient.

Ting, T.↗
NASA NTRS1976

Free vibration analysis of spinning flexible space structures

Efficient computation of natural frequencies and associated free vibration modes of spinning flexible structures is required to accurately determine the nature of interaction between the flexible structure and the attitude control system, which is vital in relating control torques to attitude angles. While structural discretization is effected by the finite element method, the resulting eigenvalue problem is solved by a combined Sturm sequence and inverse iteration procedure that yields a few specified roots and associated vectors. An eigenvalue procedure, based on a simultaneous iteration technique, provides efficient computation of the first few roots and vectors; a modal synthesis procedure proves to be useful for eigenproblem solutions of unusual structures such as spacecraft.

Gupta, K. K.↗